The present system and method are directed to measuring the three-dimensional position of colloidal particles within colloidal dispersions, and furthermore to characterizing each particle's shape, size, and optical properties, by quantitative analysis of holograms recorded through holographic video microscopy. Information obtained from this analysis can be used to characterize the colloidal particles themselves. This information also can be used to measure and assay the properties of the medium within which the particles are dispersed. In all such applications, quantitative holographic video microscopy offers substantial advantages over methods and analysis systems that have been previously described and practiced.
Particle-image velocimetry is widely applied for measuring the trajectories of colloidal particles dispersed in transparent media. Conventional implementations of particle-imaging velocimetry involve forming images of the particles using standard light microscopy and then analyzing those images through methods of computer image analysis. Such measurements and analyses typically provide information on individual particles' positions in the microscope's focal plane, but not on the particles' axial displacements relative to the focal plane. In cases where axial tracking information is extracted, the results typically have substantially poorer spatial resolution than the in-plane positions. Measurements of axial positions, furthermore, require separate calibration measurements for each particle. Such conventional particle-imaging methods generally provide little information on the particles' sizes, shapes, or compositions. The range of axial displacements over which conventional particle-imaging methods can be applied is limited by the depth of focus of the microscope because images of particles that move too far from the focal plane become too dim and diffuse to analyze.
Applications of image-based particle tracking include measuring streamlines in flowing fluids, assessing the thermodynamic stability of colloidal dispersions against aggregation and flocculation, measuring interactions among colloidal particles, measuring colloidal particles' interactions with surfaces, assessing particles' responses to external fields and forces, characterizing the particles' viscous drag characteristics, and using the particles' motions as probes of the viscoelastic and rheological properties of the embedding medium. The latter class of measurements, in which colloidal particles are used as microscopic probes of the medium's rheology, is commonly termed particle-tracking microrheology. All such applications benefit from particle-tracking techniques that offer better spatial resolution, three-dimensional tracking, and a wider axial range. Some of these applications, such as microrheology, also require information on the probe particles' characteristics, such as their radii. Typically, such particle characterization data are obtained in separate measurements.
In the particular case of microrheology, other methods are available for acquiring equivalent information on a medium's viscoelastic properties. Among these are diffusing wave spectroscopy, dynamic light scattering and interferometric particle tracking. All such methods offer superior bandwidth to those based on particle imaging. The first two do not, however, offer spatially resolved measurements, which are necessary in some applications. Interferometric particle tracking offers both excellent bandwidth and excellent tracking resolution. It can only be applied to one or two points in a sample, however, and so cannot be used for multi-point assays of rheological properties. None of these methods is suitable for analyzing the properties of inhomogeneous samples.
Individual colloidal particles typically are characterized by their shape, their size, their bulk composition, and their surface properties. Colloidal dispersions are characterized by the distributions of these quantities as well as by the overall concentration of particles. Size and shape can be assessed through electron microscopy on dried and otherwise prepared samples. Preparation can change the particles' properties, however, so that the results of such measurements might not accurately reflect the particles' characteristics in situ. Light scattering methods generally are used for in situ analysis of colloidal particles' sizes. Such measurements, however, provide a sample-averaged view of the particles in a dispersion, and generally require careful interpretation with approximate or phenomenological models for the the particles' size distribution, shapes, and refractive indexes. Commonly used commercial particle sizing instruments are based on these methods and share their limitations. These methods, furthermore, cannot be used to characterize the particular particles used in particle-tracking measurements. Other particle-sizing instruments, such as Coulter counters, similarly rely on indirect methods to measure particle sizes and cannot be applied in situ. A variety of methods also are known from measuring colloidal particles' refractive indexes. Conventional light scattering methods generally provide sample-averaged values for the refractive index and require information on the particles' sizes and shapes. A particularly effective method involves matching the refractive index of a fluid to that of the particles and then measuring the refractive index of the fluid. This method requires index-matching fluids that are compatible with the colloids and is highly limited in the range of refractive indexes that can be assessed.